# An integral problem

1. Dec 10, 2004

### sccv

I have to solve this integral

$$\int{\frac{x + 4a + b}{[x - (a + b)]^2 + c^2}}dx$$

where a, b, c are constant

Could anybody know how to solve it ?

2. Dec 11, 2004

### learningphysics

You can rewrite the integral as:

$$\int{\frac{x - (a + b)}{[x - (a + b)]^2 + c^2}}dx + \int{\frac{5a+2b}{[x - (a + b)]^2 + c^2}}dx$$

Can you solve it now looking at the two integrals separately? Do you have integral tables to work with?

3. Dec 11, 2004

### dextercioby

He doesn't need tables so solve this kind of integrals.Just well made substitutions.
Your integral should be put in the form:
$$\frac{1}{2}\int\frac{d[[x - (a + b)]^2+c^2]}{[x - (a + b)]^2 + c^2}+ (5a+2b)\int \frac{d[x-(a+b)]}{[x - (a + b)]^2 + c^2}$$

Do u see some patterns for substitutions which should bring the 2 integrals to familiar form??ln & artan in the final result??

Daniel.

4. Dec 12, 2004

### sccv

Thank you!
I also came to get those result.